Connect vertical edge to angled edge
You may use the knife project tool. Duplicate the top face of the vertical cube (Shift+D), place it between two cubes, then separate the face (P). In Object Mode select the newly created plane, then the angled cube and press Tab to enter the its Edit Mode. Go to the bottom view, press Spacebar and type Knife Project. Delete the plane. Join objects with Ctrl+J. Join meshes in Edit Mode using Bridge Edge Loops operation. Finally dissolve the horizontal edge with X-->Dissolve Edges.